We report a measurement of resonance parameters of the orbitally excited (L=1) narrow B-0 mesons in decays to B(*)+pi(-) using 1.7 fb(-1) of data collected by the CDF II detector at the Fermilab Tevatron. The mass and width of the B-2(*0) state are measured to be m(B-2(*0))=5740.2(-1.8)(+1.7)(stat)(-0.8)(+0.9)(syst) MeV/c(2) and Gamma(B-2(*0))=22.7(-3.2)(+3.8)(stat)(-10.2)(+3.2)(syst) MeV/c(2). The mass difference between the B-2(*0) and B-1(0) states is measured to be 14.9(-2.5)(+2.2)(stat)(-1.4)(+1.2)(syst) MeV/c(2), resulting in a B-1(0) mass of 5725.3(-2.2)(+1.6)(stat)(-1.5)(+1.4)(syst) MeV/c(2). This is currently the most precise measurement of the masses of these states and the first measurement of the B-2(*0) width.